Question 1 4 Marks
Visit the Australian Stock Exchange website, www.asx.com.au and from “Prices and research” drop-down menu, select “Company information”. Type in the ASX code “CSR” (CSR Limited), and find out details about the company. Also, type in the ASX code “SFR” (Sandfire Resources NL), and find out the details about that company. Both these companies belong to material sector. Information available in the ASX website will be inadequate for your purpose, you will need to search the internet for more information. Your task will be to get the opening prices of CSR and SFR shares for every quarter from January 2008 to December 2017 (unadjusted prices). If you are retrieving the monthly prices, read the values in the beginning of every Quarter (January, April, July, October) for every year from 2008 to 2017 (Total 40 observations). To provide you with some guidance as to what the unadjusted prices look like, two charts accompany this question obtained from ANZ Share Investing, Australia. After you have researched share prices and financial sector, answer the following questions:
(a) List all the quarterly opening price values in two tables, one for CSR and the other for SFR. Then construct a stem-and-leaf display with one stem value in the middle, and CSR leaves on the right side and SFR leaves on the left side. (Must use EXCEL or similar for the plot.)
1 mark
(b) Construct a relative frequency histogram for CSR and a frequency polygon for SFR on the same graph with equal class widths, the first class being “$0 to less than $1”. Use two different colours for CSR and SFR. Graph must be done in EXCEL or similar software.
1 mark
(c) Draw a bar chart of market capitals (or total assets) in 2017 (in million Australian dollars) of 6 companies listed in ASX that trade in similar products or do similar business as CSR or SFR with at least AUD100 million in market capital. Graphing must be done in EXCEL or with similar software.
1 mark
(d) If one wishes to invest in CSR or SFR, what is the market recommendation (for example, from Morningstar, Fatprophets, InvestSmart, etc.)? If you cannot find the information, what would be your recommendation based on your research of these two companies (trend, P/E ratio, dividend yield, debt and Beta)?
1 mark
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(Question 1 continued)
(Note: Use only the original values of share prices and not adjusted values.)
Question 2 4 Marks
The table below lists the prices of apartments with 2 bedrooms and 2 bathrooms sold between January and July of 2018 in Australian state capital city centres (Sydney NSW 2000, Melbourne VIC 3000, Brisbane QLD 4000, Adelaide SA 5000, Perth WA 6000, and Hobart TAS 7000). The data are available in the website
www.realestate.com.au/sold
and the prices are given in thousand Australian dollars. Consider the information as sample data since some selling prices were undisclosed.
Apartments (2 bed, 2 bath) sold between Jan and Jul 2018 in Australian state capitals.
|
Capital city
|
Prices Sold (in thousand AUD)
|
Sydney NSW 2000
|
3680, 1825, 1110, 1190, 1850, 1165, 940, 1399, 1075, 1445, 1900, 2000, 2550, 2350, 1810, 1265, 2300, 1550, 2380
|
Melbourne VIC 3000
|
643, 1320, 600, 615, 895, 700, 610, 801,830, 600, 550, 645, 690, 733, 610, 608, 525, 700, 534, 625, 770, 1325, 1142, 650, 585, 680, 770, 675, 650, 580, 570, 1667, 790, 690, 870, 515, 821, 825, 560, 470, 621
|
Brisbane QLD 4000
|
750, 452, 502, 542, 620, 490, 455, 600, 625, 527, 820, 650, 550, 498, 355, 997, 498, 450, 420, 1010, 345, 445, 760, 485, 412, 435, 505, 730, 900, 650, 510, 827, 380, 358, 375, 600, 595, 615
|
Adelaide SA 5000
|
620, 595, 360, 530, 610, 1415, 485, 691, 458, 578, 820, 600, 725, 615
|
Perth WA 6000
|
650, 535, 440, 365, 445, 440, 480, 440, 460, 490, 430, 480, 470, 545, 628, 815, 520, 490
|
Hobart TAS 7000
|
615, 893, 637, 730, 810
|
From the information provided in the table above,
(a) Compute the mean, median, first quartile, and third quartile of sold prices for each city using the exact position, (n+1)f, where
n
is the number of observations and
f
the relevant fraction for the quartile.
1 mark (Question 2 continued next page)
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(b) Compute the standard deviation, mean absolute deviation and range for each city.
1 mark
(c) Draw a box and whisker plot for the sold prices of each city and put them side by side on one graph with the same scale so that the sold prices for different cities can be compared.
(This graph must be done in EXCEL or similar software and cannot be hand-drawn.) 1mark
(d) Write a paragraph on 2 bed, 2 bath apartment prices of each city, number of apartments sold, and recent trends in apartment prices in the Australian capital cities after doing some research.
1 mark
Question 3 4 Marks
The Table below is taken from the Australian Bureau of Statistics (ABS) website
http://www.abs.gov.au/AUSSTATS/[email protected]/DetailsPage/6105.0July%202014?OpenDocument
in Employee type Excel sheet Table 6. It provides data on employment type and occupation in Australia.
Answer parts (a), (b) and (c) of the following based on the table above:
(a) What is the probability that an employee in Australia selected at random will be a Professional?
1 mark
(b) What is the probability that an employee in Australia selected at random will be a Male and a Sales worker?
1 mark
(c) Given that a female employee is working part-time, what is the probability that she belongs to the category of Clerical and administrative workers?
1 mark
(d) Visit the ABS website (Employment type, Table 6) and determine the ratio for total persons in 2013 between Owner managers of incorporated enterprises to Owner managers of unincorporated enterprises.
1 mark
Question 4 4 Marks
(a) The following data collected from the Australian Bureau of Meteorology Website (http://www.bom.gov.au/climate/data/?ref=ftr) gives the daily rainfall data (includes all forms of precipitation such as rain, drizzle, hail and snow) for the year 2017 in Hobart, Tasmania. The zero values indicate no rainfall and the left-most column gives the date. Assuming that the weekly rainfall event (number of days in a week with rainfall) follows a Poisson distribution (There are 52 weeks in a year and a week is assumed to start from Monday. The first week starts from 2 January 2017 – you are expected to visit the website and get the daily values which are not given in the table below. Part of the 52nd
week may run into 2018.):
(i) What is the probability that on any given week in a year there would be no rainfall?
1 mark
(ii) What is the probability that there will be 3 or more days of rainfall in a week?
1 mark
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(b) Assuming that the weekly total amount of rainfall (in mm) from the data provided in part (a) has a normal distribution, compute the mean and standard deviation of weekly totals.
(i) What is the probability that in a given week there will be between 3mm and 9mm of rainfall?
1 mark
(ii) What is the amount of rainfall if only 15% of the weeks have that amount of rainfall or higher? 1 mark
Question 5 4 Marks
Download Absenteeism at work data from the UCI machine learning data repository (https://archive.ics.uci.edu/ml/datasets/Absenteeism+at+work). The dataset is about unapproved absenteeism from work in hours (given in the last column of the table, column U). From the data provided, answer the questions below.
(a) Test for normality of the following variables using normal probability plot:
Transportation expense, Distance from Residence to Work, Service time, Age, and Body mass index.
2 marks
(b) Construct a 90% confidence interval for each of the variables in part (a) which can be considered as normally distributed separating the data between Absenteeism time in hours for less than 10 and Absenteeism time in hours for 10 or more. In other words, there will be two confidence interval constructions for each normally distributed variable – one for all data with less than 10 in the last column and the other for 10 or higher value in the last column. After all the confidence intervals have been constructed, identify the variable(s) which are likely to influence absenteeism from work (i.e., identify the variables where the confidence intervals do not overlap).